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The control problem of fluid catalytic cracking (FCC) units is a challenging task due to its model complexity, non-linear dynamics, constrained variables and cross-coupling interaction between inputs and outputs.
It is imperative to note that due to a large number of unknown and/or poorly constrained variables, these calculations should only be regarded as a first order approximation.
Constrained variables: (overline{P}_{text{first}}) and (overline{P}_{text{second}}) are the mean contact pressures on the first and the second sealing surface, which are the key factors to realize the sealing in SPMC, and their minimum value should be higher than 361 MPa.
Open image in new window Figure 10 Finite element model (1) Constrained variables: (overline{P}_{text{first}}) and (overline{P}_{text{second}}) are the mean contact pressures on the first and the second sealing surface, which are the key factors to realize the sealing in SPMC, and their minimum value should be higher than 361 MPa.
OK, so now we know how to find the rate of change of constrained variables with respect to each other.
The method considers a nonlinear relation between the uncertain input and the constrained variables.
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A nonlinearly improved constrained variable metric solver was used.
The weighted sum of structural mass, acoustic radiation energy of the mechanism, and energy cost of the control system is taken as the performance index, and optimization is carried out based on the modified constrained variable metric method.
Results illustrate that the Resource System's topography and Actors' socioeconomics, namely number of people at home and household land ownership, are constraining variables on land cover and help explain divergent forest cover.
Baseline values of parameters are determined by comparing model-generated output with experimental results in the literature [ 2- 8, 25] and by constraining variable values in the range of zero and one.
The final step in data pre-processing involved the normalization of the three variables to constrain variability.
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